Note that in the highly nonlocal limit \(\nu \gg 1\)  the coefficient of the third derivative term is positive, so that
solitary waves are waves of elevation, which explains why the DSWs illustrated in Figure REF  are similar
to KdV-type DSWs of elevation with solitary waves at the leading edge and linear diffractive waves at the
trailing edge, not NLS-type DSWs, which consist of waves of depression for which the positions of the solitary waves
and linear diffractive waves are reversed [1]}. The fifth derivative term is nominally of higher order,
but due to the high nonlocality \(\nu \)  the combination \(\epsilon \nu \)  can be \(O(1)\)  [2]}. This reduction
of the nematic equations to the Kawahara equation explains the presence of the resonant wavetrains seen in
Figure REF  as it has been shown that for the Kawahara equation (REF ) linear diffractive waves
resonate with the DSW if \(\mu > 0\) . In this case, the Kawahara DSW can be a RDSW, CDSW or TDSW, depending on the
value of \(\mu \) . The vacuum cases of Figures REF (d) and (e) cannot occur for a KdV DSW. They arise
for the nematic DSW and NLS-type DSWs due to the requirement \(|u| \ge 0\) . The Kawahara equation reduction of the full
nematic equations will be used in Sections – to derive the DSW solution as the cases studied
there correspond to a small jump height \(u_{-} - u_{+}\) .
